Correlation preserving map between bipartite states and temporal evolutions

TL;DR

This paper extends the Jamiolkowski isomorphism to demonstrate that spatial correlations in bipartite quantum states are equivalent to temporal correlations in local systems, with implications for decoherence, inequalities, and large system analysis.

Contribution

It generalizes the correlation map between bipartite states and temporal evolutions, revealing a fundamental equivalence observable via weak measurements.

Findings

Spatial and temporal correlations are equivalent under the extended map.

Weak measurements can observe these correlations.

Implications for decoherence, inequalities, and large system analysis.

Abstract

The Hilbert space formalism of quantum theory manifests a map between bipartite states and time evolutions, known as Jamiolkowski isomorphism. We extend this map in a physical setting to prove the equality of spatial correlations in bipartite systems and temporal correlations in local systems. We show that these correlations can be observed using weak measurements. This result has several practical and conceptual implications such as manifestation of state independent decoherence, the correspondence between Bell and Leggett-Garg inequalities, multipartite systems, the statistical properties of evolutions in large systems, and computational gain, in evaluation of spatial correlations in large systems.